Yes, they might be able to. If there are any watermarks or unique visual elements that change when screenshot, it could be a giveaway. Also, if the story has some kind of anti - screenshot protection, it could alert the owner.
It depends on various factors. For example, if the story has a distinct style, color, or pattern, and the screenshot somehow alters or misses some of these details, it can be detected. However, if you take the screenshot carefully and it looks like a normal view of the story, it may be hard to tell. Moreover, some platforms have features that can detect unauthorized screenshots.
Often, it's not easy for someone to know if you've taken a screenshot of their story. But if the story contains elements that are difficult to replicate exactly in a screenshot, like interactive features or animations that don't show up properly in the screenshot, the owner may suspect. Also, if the screenshot is shared in a way that comes back to the original story's context, it could raise questions.